What should I do?

Sometime in the next few months I will be heading to New York City. Long story short (not if you know me....) my very favorite band has an annual Christmas festival in Chicago but in 2010 they had to cancel it because their frontman is in the cast of Spider-Man Turn off the Dark and couldn't get away from the play for the three days of their Christmas show. So they are planning a "replacement" show in NYC. Planning, present tense, which is why I still don't now when I'm going to be making my trip.
Of course because I will be in the city and am a huge theater geek, I will be seeing a performance of Spider-Man, plus whatever the band has planned for us, but I will probably have some free time. I don't like doing "touristy" things, rather experiencing new places from the natives' point of view. So what are some great things to do in NYC/Manhattan in the Spring?